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MHT CET202314 May 2023Morning ShiftMathematicsQuadratic EquationActual

The equation x^3+x-1=0 has

Options

  1. Ano real root.
  2. Bexactly two real roots.
  3. Cexactly one real root.
  4. Dmore than two real roots.

Correct answer

C. exactly one real root.

Step-by-step solution

Let f (x)=x^3+x-1 A root of f (x) exists, if f (x)=0 for at least one value of x . aligned & f (0)=-1 0 aligned By intermediate value theorem, there has to be a point ' c ' between 0 and 1 such that f (x)=0 . The given equation has exactly one real root. Alternate Method: Let f (x)=x^3+x-1 array ll f ^ (x)=3 x^2+1 f ^ (x)>0 x R array f (x) is an increasing function. f (x) intersects X -axis at only one point. The given equation has exactly one real root.

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